Raghav buys a shop for rs 120000. He pays half of amount in cash and agreed to pay the balance in 12 annual instalments of rs 5000 each.if the rate of interest is 12℅ and he pays with the instalments the interest due on the unpaid amount , find the total cost of the shop?
Answers
Answer:
Step-by-step explanation:
Given that Raghav buys a shop for 120000.
He pays half of the amount in cash = 1/2 * 120000
= 60000.
Balance amount to be paid = 120000 - 60000 = 60000.
Given that amount of each installment = 5000.
He agrees to pay the balance in 12 annual installments with interest of 12%.
1. Amount of the first installment = 5000 + 12/100 * 60000
= 5000 + 600 * 12
= 5000 + 7200
= 12200.
2. Amount of the second installment = 5000 + 12/100 * (60000 - 5000)
= 5000 + 12/100 * 55000
= 5000 + 550 * 12
= 5000 + 6600
= 11600.
So. the amount paid for installment is 12200,11600.......It forms an AP.
The 1st term a = 12200
Common Difference d = 11600 - 12200
= -600.
The number of terms n = 12.
We know that sum of n terms = n/2(2a + (n-1)* d)
Therefore the total cost of the shop = 60000 + 12/2(2(12200) + (12-1) * (-600))
= 60000 + 6(24400 - 6600)
= 60000 + 6 * 17800
= 60000 + 106800
= 166800.
The total cost of the shop = 166800.
Hope this helps!
Balance amount to be paid in installments = Rs 120000 – Rs 60000 = Rs 60000
Amount of each installment = Rs 5000
Amount of first installment
= Rs 5000 + Interest paid on unpaid amount Rs 60000
Amount of second installment
= Rs 5000 + Interest on unpaid amount of Rs 55000
Amount of third installment
= Rs 5000 + Interest on unpaid amount of Rs 50000
Rs 12200, Rs 11600, Rs 11000,..... forms an A.P.
First term = Rs 12200
Common difference = Rs 11600 – Rs 12200 = – Rs 600
Total cost of the shop
= Rs 60000 + Sum of 12 installments
= Rs 60000 + Rs 6 (24400 – 6600)
= Rs 60000 + Rs 106800
= Rs 166800
Thus, the total cost of the shop is Rs 166800